Title: Auf Wiedersehen Surfaces, Revisited
Speaker: Robert Bryant
Speaker Info: MSRI and University of California, Berkeley
It has been known for over a century that there are many Riemannian metrics on the 2-sphere with the property that all of their geodesics are closed. Zoll, a student of Hilbert, constructed an infinite dimensional family of surfaces of rotation with this property. Following ideas of Funk, Guillemin proved that these metrics on the 2-sphere are essentially parametrized by the odd functions on the round 2-sphere.Date: Wednesday, March 10, 2010
These ideas can also be applied to the understanding of Finsler metrics on the 2-sphere whose Finsler-Gauss curvature is constant, as will be explained in the talk. This leads, via the recent work of LeBrun and Mason, to a resolution of a basic problem in Finsler geometry: to describe such Finsler metrics on the 2-sphere.
In this talk, no knowledge of Finsler geometry will be assumed, only a very basic understanding of curves and surfaces. The history of the problem will be discussed, and numerous examples will be given to illustrate the underlying ideas.